ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 487 



two dimensions however complicated or irregular that 

 motion might appear to be could be mathematically- 

 represented or calculated by the superposition or addition 

 of a larger or smaller number of simple periodic motions ; 

 as it were analysed and dissected into these simple move- 

 ments, just as any number can be looked upon as made 

 up by the addition of others say of prime numbers. 

 Now, it was also known that sounds were produced by 

 wave-like tremors of the air set going by the vibrations 

 of strings or other sounding musical instruments ; further, 

 that definite musical notes were absorbed or transmitted 

 by neighbouring sounding bodies according as these were 

 in or out of tune with the vibrating source of sound. 

 This is the well-known phenomenon of resonance. Ohm 1 

 had applied Fourier's mathematical analysis to the ex- 

 planation of the partial notes, the ground tone and the 

 harmonic overtones (or upper partial tones), of which 

 musical 2 sounds are made up. Helmholtz invented a 



1 Geo. S. Ohm, the same to 

 whom we are indebted for the 

 well-known law which obtains in 

 electric currents, published in 1843 

 a paper in Poggendorf s ' Annalen ' 

 (reprinted in ' Gesammelte Ab- 

 handlungen,' 1892, p. 575), "On 

 the definition of a tone and the 

 theory of the siren," in which he 

 applied the mathematical methods 

 introduced by Fourier in his ' The- 

 orie analytique de la Chaleur' 

 (1822) : as he had already done in 

 his earlier work on the galvanic 

 current (1827). In fact, Ohm was 

 one of the first to recognise the 

 value of Fourier's conceptions in 

 contradistinction from Laplace's, 

 which were bound up with certain 

 hypothetical notions as to the 

 molecular constitution of bodies. 



See the introduction to his treatise 

 on the galvanic current (' Ges. 

 Werke,' p. 63). 



2 Cagniard de la Tour had in- 

 vented (1819) and Seebeck the 

 younger had improved (1841) the 

 first mechanical counter for the 

 frequencies of musical sounds, the 

 siren ; and the latter as well as 

 Duhamel had studied the com- 

 position of such sounds out of their 

 elements or simple notes. A sug- 

 gestion had been thrown out as to 

 the part played by the upper 

 partial tones which accompanied 

 the ground tone. Helmholtz treats 

 first of this subject in a lecture 

 (1857), reprinted in ' Vortriige und 

 Reden,' vol. i. p. 79, dealing with 

 " the psychological causes of musi- 

 cal harmony." 



